an:01716578
Zbl 0999.15009
Lu, Linzhang
Perron complement and Perron root
EN
Linear Algebra Appl. 341, No. 1-3, 239-248 (2002).
00082109
2002
j
15A18 15B48 65F15
Perron complement; spectral radius; Perron root; algorithm
For a nonnegative irreducible matrix \(A\) the well known Perron complement is generalized. The main theorem that describes the relation between the generalized Perron complement of \(A\) and its Perron root, i.e. the spectral radius \(\rho(A)\) of \(A\), is stated. On several examples, it is shown how the use of the theorem can improve both lower and upper bounds for \(\rho(A)\). Combining the theorem with other known methods gives the algorithm for a computation of the value of \(\rho(A)\).
Jitka Drko??ova (Praha)